Implementing Mathematical Modelling with Calculus of Variations to Design a Disaster Tent

Year 2024, Volume: 11 Issue: 2, 199 - 212, 31.12.2024

Fatma Aslan-tutak , Ozan Guven

https://doi.org/10.59409/ojer.1587040

Abstract

This manuscript shares results from a mathematical modelling project developed by a mathematics educator and a high school student to solve a real-life problem; durable disaster tents. The authors worked together to first design a tent, CaTent, by implementing biomimicry with design thinking. Through the process of mathematical modelling, the authors mathematise the problem with catenary which can be obtained by solving a calculus of variations problem. Then, reaching the equation for catenary curve modelling the poles of CaTent, the length of a pole is obtained, approximately 7.2834 meters. The total length of three poles necessary for a CaTent would be 21.8503 meters approximately, while the total amount of poles needed for a common disaster tent would be approximately 40.32 meters.

Keywords

Mathematical modelling, calculus of variations, catenary, design thinking, biomimicry

Ethical Statement

There were no data collection with humans, so ethical approval was not necessary.

References

• Aslan-Tutak, F. (2020). Matematik eğitiminde disiplinlerarası etkinlikler ve STEM eğitimi. In Y. Dede, M. F. Doğan, & F. Aslan-Tutak (Eds.), Matematik eğitiminde etkinlikler ve uygulamaları (pp. 97-124). Pegem Publishing.
• American Scientist. (2018, February 2). The perfect dome. American Scientist. https://www.americanscientist.org/article/the-perfect-dome
• Biomimicry Institute. (2019, April 19). What is biomimicry? Biomimicry Institute. https://biomimicry.org/what-is-biomimicry/
• Cornell University. (2023, February 16). Hanging cables and spider threads. Cornell University. https://arxiv.org/abs/2302.09054
• Chen, D. A., Klotz, L. E., & Ross, B. E. (2016). Mathematically characterizing natural systems for adaptable, biomimetic design. Procedia Engineering, 145, 497-503.
• Girgin, D. (2021). A sustainable learning approach: Design thinking in teacher education. International Journal of Curriculum and Instruction, 13(1), 359–382.
• Gohnert, M., & Bradley, R. (2022). Membrane stress equations for a catenary dome with a variation in wall thickness. Engineering Structures, 253, 113793. https://doi.org/10.1016/j.engstruct.2021.113793
• Hass, J., Heil, C., & Weir, M. D. (2000). Thomas' calculus: Early transcendentals (11th ed.). Pearson.
• Karataş Aydın, F. İ., & Aslan-Tutak, F. (2023). Eğitim uygulamalarında tasarım odaklı düşünmeye yönelik çerçeve. In D. Girgin & Z. Toker (Eds.), Eğitimde tasarım odaklı düşünme yaklaşımı ve uygulama örnekleri (pp. 69-106). Nobel.
• Sanne, F., Risheim, I., & Impelluso, T. J. (2019). Inspiring engineering in the K12: Biomimicry as a bridge between math and biology. ASME International Mechanical Engineering Congress and Exposition, American Society of Mechanical Engineers, Salt Lake City, Utah, USA.
• Schaap, S., Vos, P., & Goedhart, M. (2011). Students overcoming blockages while building a mathematical model: Exploring a framework. In G. Kaiser, W. Blum, R. B. Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling: International perspectives on the teaching and learning of mathematical modelling, vol. 1 (pp. 137–146). Springer.
• Scheer, A., Noweski, C., & Meinel, C. (2012). Transforming constructivist learning into action: Design thinking in education. Design and Technology Education: An International Journal, 17(3), 8-19.
• Sol, M., Giménez, J., & Rosich, N. (2011). Project modelling routes in 12–16-year-old pupils. In G. Kaiser, W. Blum, R. B. Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling: The 14th ICMTA study (pp. 231–240). Springer.
• Stanford University. (2024). d.school. Stanford University. https://dschool.stanford.edu/about